chore(CPlusPlus): add Matrix Chain Multiplication to Dynamic Programming (#410)

Co-authored-by: Arsenic <54987647+Arsenic-ATG@users.noreply.github.com>

algorithms/CPlusPlus/Dynamic-Programming/matrix-chain-multiplication.cpp

@@ -0,0 +1,56 @@
+// Matrix Chain Multiplicatin - Memorization-Approuch
+
+#include <bits/stdc++.h>
+using namespace std;
+
+// Function for matrix chain multiplication
+int matrixChainMulti(vector<int> &arr, const int i, const int j, vector<vector<int>> &dp)
+{
+    if (i >= j)
+        return 0;
+
+    if (dp[i][j] != -1)
+        return dp[i][j];
+
+    int countMin = INT_MAX;
+    for (int k = i; k < j; k++)
+    {
+        int temp_ans = matrixChainMulti(arr, i, k, dp) + matrixChainMulti(arr, k + 1, j, dp) + (arr[i - 1] * arr[k] * arr[j]);
+        if (temp_ans < countMin)
+            countMin = temp_ans;
+    }
+    return dp[i][j] = countMin;
+}
+
+// Driver Code
+int main()
+{
+    // dp table initialized with -1
+    vector<vector<int>> dp(1001, vector<int>(1001, -1));
+
+    int n;
+    cout << "Enter the array size." << endl;
+    cin >> n;
+    vector<int> arr(n);
+    cout << "Enter all the array elements." << endl;
+    for (int i = 0; i < n; i++)
+        cin >> arr[i];
+
+    cout << "Minimum number of multiplications is" << endl;
+    cout << matrixChainMulti(arr, 1, n - 1, dp) << endl;
+}
+
+/*
+ * Time Complexity: O(N^3)
+ * Auxiliary Space: O(N^2)
+
+ * Input:
+ *  n = 4
+ *  arr = {10, 30, 5, 60}
+ *  Output: 4500
+ * Explanation: The matrices have dimensions 
+ * 10*30, 30*5, 5*60. Say the matrices are A, B 
+ * and C. Out of all possible combinations,the
+ * most efficient way is (A*B)*C. The 
+ * number of multiplications are: 10*30*5 + 10*5*60 = 4500.
+ */

algorithms/CPlusPlus/README.md

@@ -18,6 +18,7 @@
 1. [Longest Common Subsequence](Dynamic-Programming/longest-common-subsequence.cpp)
 2. [Longest Common Substring](Dynamic-Programming/longest-common-substring.cpp)
 3. [0/1-knapsack](Dynamic-Programming/01-knapsack-bottom-up.cpp)
+4. [Matrix chain Multiplication](Dynamic-Programming/matrix-chain-multiplication.cpp)
 
 ## Graphs
 
@@ -60,7 +61,6 @@
 
 3. [Stack using Array](Stacks/stack-using-array.cpp)
 
-
 ## Sorting
 
 1. [Bubble Sort](Sorting/bubble-sort.cpp)
@@ -106,4 +106,5 @@
 4. [Fibonacci Series](Maths/fibonaccci-series.cpp)
 
 # Recursion
+
 1. [Tower of Hanoi](Recursion/towerofHanoi.cpp)